/C

# clogf, clog, clogl

Defined in header <complex.h>
float complex       clogf( float complex z );
(1) (since C99)
double complex      clog( double complex z );
(2) (since C99)
long double complex clogl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define log( z )
(4) (since C99)
1-3) Computes the complex natural (base-e) logarithm of z with branch cut along the negative real axis.
4) Type-generic macro: If z has type long double complex, clogl is called. if z has type double complex, clog is called, if z has type float complex, clogf is called. If z is real or integer, then the macro invokes the corresponding real function (logf, log, logl). If z is imaginary, the corresponding complex number version is called.

### Parameters

 z - complex argument

### Return value

If no errors occur, the complex natural logarithm of z is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

### Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• The function is continuous onto the branch cut taking into account the sign of imaginary part
• clog(conj(z)) == conj(clog(z))
• If z is -0+0i, the result is -∞+πi and FE_DIVBYZERO is raised
• If z is +0+0i, the result is -∞+0i and FE_DIVBYZERO is raised
• If z is x+∞i (for any finite x), the result is +∞+πi/2
• If z is x+NaNi (for any finite x), the result is NaN+NaNi and FE_INVALID may be raised
• If z is -∞+yi (for any finite positive y), the result is +∞+πi
• If z is +∞+yi (for any finite positive y), the result is +∞+0i
• If z is -∞+∞i, the result is +∞+3πi/4
• If z is +∞+∞i, the result is +∞+πi/4
• If z is ±∞+NaNi, the result is +∞+NaNi
• If z is NaN+yi (for any finite y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+∞i, the result is +∞+NaNi
• If z is NaN+NaNi, the result is NaN+NaNi

The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ

### Example

#include <stdio.h>
#include <math.h>
#include <complex.h>

int main(void)
{
double complex z = clog(I); // r = 1, θ = pi/2
printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z));

double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2*I); // r = 1, θ = pi/4
printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2));

double complex z3 = clog(-1); // r = 1, θ = pi
printf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3));

double complex z4 = clog(conj(-1)); // or clog(CMPLX(-1, -0.0)) in C11
printf("log(-1-0i) (the other side of the cut) = %.1f%+fi\n", creal(z4), cimag(z4));
}

Output:

2*log(i) = 0.0+3.141593i
4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593i
log(-1+0i) = 0.0+3.141593i
log(-1-0i) (the other side of the cut) = 0.0-3.141593i
• C11 standard (ISO/IEC 9899:2011):
• 7.3.7.2 The clog functions (p: 195)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.3.2 The clog functions (p: 543-544)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.7.2 The clog functions (p: 176-177)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.3.2 The clog functions (p: 478-479)
• G.7 Type-generic math <tgmath.h> (p: 480)

 cexpcexpfcexpl (C99)(C99)(C99) computes the complex base-e exponential (function) loglogflogl (C99)(C99) computes natural (base-e) logarithm ($${\small \ln{x} }$$ln(x)) (function) C++ documentation for log